Rotation and Screw Axes

Click on buttons to display rotation or screw axes

[2]  2-fold rotation axis
[21] 2-fold screw axis

[3]  3-fold rotation axis
[31] 3-fold screw axis
[32] 3-fold screw axis

[4]  4-fold rotation axis
[41] 4-fold screw axis
[42] 4-fold screw axis
[43] 4-fold screw axis

[6]  6-fold rotation axis
[61] 6-fold screw axis
[62] 6-fold screw axis
[63] 6-fold screw axis
[64] 6-fold screw axis
[65] 6-fold screw axis

Axis perpendicular to screen

Screw axes, like glide planes, are translation operators. Here, a rotation is combined with a translation.

The screw axis symbol, nm has a number (n), which gives the rotation, and a subscript (m), which describes the translation.

An n-fold screw axis has rotation elements of 2p/n, where n = 1, 2, 3, 4 or 6. The translation component, m, in the screw axis symbol nm is m/n times the lattice vector in the direction of the axis. Hence for 65, the translation is 5/6 times the lattice vector along the axis for each rotation of 2p/6.

The symbols nm and nm-n are enantiomorphous, describing mirror images. As examples, look at 41 and 43.

Any crystallographic direction may be a 1-fold screw axis, and it is sometimes helpful to show that a particular direction is not a symmetry direction by notating this as a 1-fold axis.

Click and hold the mouse over the CHIME image, then move the mouse to rotate. The rotation axis is shown by the central grey line. Units which undergo rotation and translation are shown by green spheres. The grey lines outline features of the symmetry.